Hydrodynamics of spin transport in the Haldane-Shastry chain

TL;DR

This paper develops a hydrodynamic theory for spin transport in the Haldane-Shastry chain, providing analytical results and corroborating them with exact and known limits across temperature regimes.

Contribution

It introduces a comprehensive hydrodynamic framework for the Haldane-Shastry chain, combining kinetic theory and Bethe ansatz to derive new analytical expressions for spin transport.

Findings

Analytical relaxation expressions for weak-domain-wall initial conditions

Predictions for the spin Drude weight validated against microscopic calculations

Long-wavelength spin structure factor dynamics interpolating between known limits

Abstract

We use kinetic theory and the thermodynamic Bethe ansatz to derive the hydrodynamics of spin transport in the Haldane-Shastry chain. We obtain analytical expressions for relaxation from weak-domain-wall initial conditions and corresponding predictions for the spin Drude weight. We corroborate the latter against an exact microscopic calculation at infinite temperature and Luttinger-liquid expectations at zero temperature. We further obtain an analytical expression for the long-wavelength dynamics of the longitudinal spin structure factor at all fillings and temperatures. We show that the latter interpolates between an empirically exact expression that we have found at infinite temperature and the long-wavelength limit of the Haldane-Zirnbauer formula at zero temperature.